MATHEMATICAL MODELING OF POROUS GEOMETRICALLY NONLINEAR METAL NANO-PLATES TAKING INTO ACCOUNT MOISTURE

Abstract

Link for citation: Krysko A.V., Kalutsky L.A., Zakharova A.A., Krysko V.A. Mathematical modeling of porous geometrically nonlinear metal nano-plates taking into account moisture. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 9, рр. 36-48. In Rus. The relevance.  The study of stress-strain behaviour and bearing capacity of porous metallic nanoplates, especially under extreme conditions and taking into account large deformations, is of great importance. These structures have a wide range of practical applications, for example, to clean solid fractions in wells during their setting up and to ensure fluid flow during operation. In addition, porous metal filters in the form of plates can serve as effective filters for removing solids from production wellbores, especially in the bottomhole zone. The versatility of these materials extends to various industries including aerospace, medical and instrumentation, indicating their potential to solve critical problems and advance technologies in various fields. The main aim of the research is to develop a new model of porous nanoplates, taking into account moisture, which would describe the real work of the studied objects in the oil and gas industry and other industries; to construct the efficient and fast methods for studying porous metallic nanoplates. Methods: variational iterations method, an extended Kantorovich method, which has high accuracy of solution of nonlinear problems and fast performance. The correctness of application of this method is conditioned by the proof of its convergence theorems belonging to the authors. In addition, the obtained solutions are compared with the solutions obtained by the Bubnov–Galerkin method in higher approximations and by the finite difference method of the second order of accuracy, as well as with the solutions obtained by other authors. Results. A model of porous flexible nanoplates is constructed taking into account moisture. Nano effects are described by the modified moment theory of elasticity. The method of variational iterations is further developed for the study of the stress-strain state of porous metallic nanoplates at large deflections. The paper analyzes the types of material porosity, size-dependent nano parameter, moisture distribution, porosity index and boundary conditions on the bearing capacity of porous metal plates. The type of porous material with the highest bearing capacity is identified.